Accelerating the induced dimension reduction method using spectral information

DOI10.1016/j.cam.2018.06.014zbMath1408.65011OpenAlexW2809037386WikidataQ129625005 ScholiaQ129625005MaRDI QIDQ1789683

R. Astudillo, J. M. de Gier, Martin B. van Gijzen

Publication date: 10 October 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://resolver.tudelft.nl/uuid:c7d0bcb1-1ed4-4290-8bd8-5c1391998fbc

zbMATH Keywords

induced dimension reduction methoddeflated and augmented Krylov methodsequence of systems of linear equationssparse system of linear equations

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Uses Software

• MatrixMarket
• Algorithm 913

Cites Work

• Unnamed Item
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• A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Fast Leja points
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• Minimizing synchronization in IDR (s )
• Algorithm 913
• Interpreting IDR as a Petrov–Galerkin Method
• Exploiting BiCGstab($\ell$) Strategies to Induce Dimension Reduction
• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems
• IDR(s): A Family of Simple and Fast Algorithms for Solving Large Nonsymmetric Systems of Linear Equations
• Recycling Krylov Subspaces for Sequences of Linear Systems
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Truncation Strategies for Optimal Krylov Subspace Methods
• Implicitly Restarted GMRES and Arnoldi Methods for Nonsymmetric Systems of Equations
• ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
• A Restarted GMRES Method Augmented with Eigenvectors
• On the Convergence Behavior of IDR($s$) and Related Methods
• Block GMRES Method with Inexact Breakdowns and Deflated Restarting
• The principle of minimized iterations in the solution of the matrix eigenvalue problem

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